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2011

On the minimal monochromatic K4-density

Sperfeld, Konrad

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We use Razborov's flag algebra method to show a new asymptotic lower bound for the minimal density $m_4$ of monochromatic $K_4$'s in any 2-coloring of the edges of the complete graph $K_n$ on $n$ vertices.

The hitherto best known lower bound was obtained by Giraud, who proved that m_4>1/46, whereas the best known upper bound by Thomason states that m_4<1/33.
We can show that m_4>1/35.

On the minimal monochromatic K4-density · Around

Built on

A. W. Goodman On sets of aquaintances and strangers at any party
1959
Earlier work this paper cites.
Paul Erdös On the number of complete subgraphs contained in certain graphs
1962
Earlier work this paper cites.
Guy Giraud Sur le problème de Goodman pour les Quadrangles et la Majoration des Nombres de Ramsey
1979
Earlier work this paper cites.

Similar

Andrew Thomason A disproof of a conjecture of Erdös in Ramsey theory
1989
Cited alongside, same era.
Andrew Thomason Graph products and monochromatic multiplicities
1997
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Alexander A. Razborov Flag algebras
2007
Cited alongside, same era.

Then

Alexander A. Razborov On 3 3 -Hypergraphs with forbidden 4 4 -vertex configurations
2010
Later among the works it cites.
J. Wolf The minimum number of monochromatic 4-term progressions in ℤ p \mathbb{Z}_{p}
Original
2010
Later among the works it cites.
H. Hatami, J. Hladký, D. Král’, S. Norine, A. A. Razborov Non-three colorable common graphs exist
Original
2011
Closest in time.

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